New
New
Year 6

Two congruent triangles can be arranged to compose a parallelogram

I can explain how two congruent triangles can arranged to compose a parallelogram.

New
New
Year 6

Two congruent triangles can be arranged to compose a parallelogram

I can explain how two congruent triangles can arranged to compose a parallelogram.

Lesson details

Key learning points

  1. The area of a triangle is equal to half the area of the parallelogram you create from 2 congruent triangles.
  2. Any parallelogram can be decomposed into two congruent triangles.

Common misconception

If pupils do not cut a parallelogram from vertex to opposite vertex, they will end up with either two non-congruent shapes or two congruent quadrilaterals.

Modelling is key and this is a useful time to revisit the concept of a shape's diagonal, that is, a line connecting vertex to a non-adjacent vertex.

Keywords

  • Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

  • Parallelogram - A parallelogram is a quadrilateral with two pairs of parallel and equal sides.

In this lesson pupils will need to be familiar with triangle types and their properties. Consider how you might scaffold this knowledge for learners if required.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Which of these are properties of all triangles?
All sides must be equal.
Four sides.
Correct answer: Three interior angles.
3-dimensional.
Correct answer: All sides are straight.
Q2.
Match the triangle with the correct property.
Correct Answer:Equilateral,Three equal sides.

Three equal sides.

Correct Answer:Isosceles,Two equal sides and one different.

Two equal sides and one different.

Correct Answer:Scalene,No equal sides.

No equal sides.

Correct Answer:Right-angled,One pair of perpendicular sides.

One pair of perpendicular sides.

Q3.
Which of these polygons is also classified as a parallelogram?
Triangle
Correct answer: Square
Correct answer: Rectangle
Trapezium
Q4.
Which of these statements apply to all parallelograms?
Correct answer: Opposite angles are equal.
Opposite angles are different.
Correct answer: Opposite sides are equal in length.
Opposite sides are different in length.
Q5.
Which of these statements is true about these shapes?
An image in a quiz
Correct answer: Both shapes are parallelograms.
Shape a is a parallelogram but Shape b is not.
Neither shape is a parallelogram.
Q6.
The two compound shapes have been composed of identical smaller shapes. Which of these statements is true?
An image in a quiz
Correct answer: The shapes have the same area.
The area of a is greater than the area of b.
The area of b is greater than the area of a.
Correct answer: They are both compound shapes.

6 Questions

Q1.
If two shapes are congruent, what does this mean?
Correct answer: They are the same type of shape.
They are different types of shape.
Correct answer: They are the same size.
They are different sizes.
Q2.
Which of these triangles are congruent?
An image in a quiz
Correct answer: a
b
Correct answer: c
d
Q3.
Which of these statements could be true of two congruent shapes?
Correct answer: They could be the same shape but rotated.
Correct answer: They could be the same shape but reflected.
They must be identical in every way including their position.
Q4.
Which of the statements are true?
A triangle can be composed from two parallelograms.
Correct answer: A parallelogram can be composed from two congruent triangles.
Correct answer: A parallelogram can be decomposed into two congruent triangles.
Q5.
This parallelogram has been decomposed into two congruent triangles. What type of triangle is each part?
An image in a quiz
equilateral
isosceles
Correct answer: scalene
Q6.
Which of these quadrilaterals cannot be decomposed into two congruent triangles?
Parallelogram
Rectangle
Square
Rhombus
Correct answer: Trapezium